A health club charges a $20 one-time sign-up fee and a monthly membership fee of $39 per month. Find the rate of change

Answer:

20,80

Step-by-step explanation:

\(Let\ Abduls\ present\ age\ be\ x\\His\ Grandfather's\ present\ age\ = 4x\\\\Abdul's\ age\ before\ 10\ years=x-10\\His\ Grandfather's\ age\ before\ 10\ years =4x-10\\\\We\ are\ given\ that\ ,\\Abdul's\ Grandfather's\ age\ before\ 10\ years = 7 * Abdul's\ age\ before\ 10\ years\\Hence, \\4x-10=7(x-10)\\4x-10=7x-70\\-10+70=7x-4x\\60=3x\\x=20\\Hence,\\Abduls\ present\ age\ =20\\His\ grandfather's\ present\ age\ = 4*20=80\)

Answer:

Abdul's age=20 y/o

Grandpa's age=80y/o

Step-by-step explanation:

let Abdul's age be 'x'

so, grandpa's age=4x

Grandpa's age 10 yrs ago= 4x-10

according to the question, grandpa's age 1o yrs ago=7(x-10)

so, 4x-10=7(x-10)

     4x-10=7x-70

by substituting,

     70-10=7x-3x

     60=3x

     60/3=x

      20y/o=x

so, 4x=20*4=80 y/o

The volume of the triangular prism is 60 cm³

A solid figure is a three dimensional shape that has length, width and height. Example of solid figures are cube, pyramid, prism, sphere and so on.

The volume of a triangular prism is given as:

Volume = area of base * height

The area of the prism base = (1/2) * base * height = 1/2 * 5 * 8 = 20 cm²

Volume = area of base * height = 20 cm² * 3 cm = 60 cm³

The volume is 60 cm³

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Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Answer:

Step-by-step explanation:

From the given information:

the null and alternative hypotheses in symbolic form for this claim can be computed as:

\(H_o:\mu = 18 \\ \\ H_a : \mu > 18\)

Mean = \(\dfrac{18.5+18.2+20+21.3+17.9+17.9+18.1+17.5+20+18}{10}\)

Mean = 18.74

Standard deviation  \(\sigma = \sqrt{\dfrac{\sum(x_i - \mu)^2}{N}}\)

Standard deviation  \(\sigma = \sqrt{\dfrac{(18.5 - 18.74)^2+(18.2 - 18.74)^2+(20 - 18.74)^2+...+(18 - 18.74)^2}{10}}\)

Standard deviation \(\sigma\)   = 1.18

The test statistics can be computed as follows:

\(Z= \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}\)

\(Z= \dfrac{18.6- 18}{\dfrac{1.18}{\sqrt{10}}}\)

\(Z= \dfrac{0.6}{\dfrac{1.18}{3.162}}\)

Z = 1.6078

Z = 1.61

Degree of freedom = n -1

Degree of freedom = 10 -1

Degree of freedom = 9

Using t - calculator at Z = 1.6078 and df = 9

The P - value = 0.0712

Answer:

2

Step-by-step explanation:

The inverse Laplace transform of f(s) is:

f(t) = (-1/960)*δ'(t) - (1/30)sin(t) - (1/10)sin(2t) + (1/240)sin(3t)

We can write f(s) as:

f(s) = 5040s^7 - 5s

We can use partial fraction decomposition to simplify f(s):

f(s) = 5s - 5040s^7

= 5s - 5040s(s^2 + 1)(s^2 + 4)(s^2 + 9)

We can now write f(s) as:

f(s) = A1s + A2(s^2 + 1) + A3*(s^2 + 4) + A4*(s^2 + 9)

where A1, A2, A3, and A4 are constants that we need to solve for.

Multiplying both sides by the denominator (s^2 + 1)(s^2 + 4)(s^2 + 9) and simplifying, we get:

5s = A1*(s^2 + 4)(s^2 + 9) + A2(s^2 + 1)(s^2 + 9) + A3(s^2 + 1)(s^2 + 4) + A4(s^2 + 1)*(s^2 + 4)

We can solve for A1, A2, A3, and A4 by plugging in convenient values of s. For example, plugging in s = 0 gives:

0 = A294 + A314 + A414

Plugging in s = ±i gives:

±5i = A1*(-15)(80) + A2(2)(17) + A3(5)(17) + A4(5)*(80)

±5i = -1200A1 + 34A2 + 85A3 + 400A4

Solving for A1, A2, A3, and A4, we get:

A1 = -1/960

A2 = -1/30

A3 = -1/10

A4 = 1/240

Therefore, we can write f(s) as:

f(s) = (-1/960)s + (-1/30)(s^2 + 1) + (-1/10)(s^2 + 4) + (1/240)(s^2 + 9)

Taking the inverse Laplace transform of each term, we get:

f(t) = (-1/960)*δ'(t) - (1/30)sin(t) - (1/10)sin(2t) + (1/240)sin(3t)

where δ'(t) is the derivative of the Dirac delta function.

Therefore, the inverse Laplace transform of f(s) is:

f(t) = (-1/960)*δ'(t) - (1/30)sin(t) - (1/10)sin(2t) + (1/240)sin(3t)

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Answer:

The answer would be 15yd^2.

Step-by-step explanation:

The area of a triangle is found by...

A = (L*H) / 2

L = length

H = height

Answer:

15.0 yd

Step-by-step explanation:

 A=  h b/2 = 3·10/2=15

Answer:

∠ C = 100°

Step-by-step explanation:

since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.

consider the angle inside the triangle to the left of 140°

this angle and 140° are a linear pair and sum to 180°

angle + 140° = 180° ( subtract 140° from both sides )

angle = 40°

then the angle on the left of the triangle = 40° ( base angles congruent )

the sum of the angles in a triangle = 180° , so

∠ C + 40° + 40° = 180°

∠ C + 80° = 180° ( subtract 80° from both sides )

∠ C = 100°

Answer:

2.4166667 = 24166667/

10000000

= 2.4166667

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

9x+7+10x+8+70=180

19x+85=180

19x=95

x=5

9(5)+7=52

180-110=70

Answer:

A proportion is an equality of two ratios.

...

Things to remember

Determine whether the ratio is part to part or part to whole.

Calculate the parts and the whole if needed.

Plug values into the ratio.

Simplify the ratio if needed. Integer-to-integer ratios are preferred.

Answer:

(–2, 3), (–1, 0), and (0, –3)

Step-by-step explanation:

Answer:

it's (–2, 3), (–1, 0), and (0, –3)

Step-by-step explanation:

Answer:

Its answer d

Step-by-step explanation:

I took the quiz  

A 2-column table with 4 rows. Column 1 is labeled x with entries 2, 4, 6, 8. Column 2 is labeled y with entries negative 4, negative 12, negative 20, negative 28.

A 2-column table with 4 rows. Column 1 is labeled x with entries 2, 4, 6, and 8. Column 2 is labeled y with entries negative 4, negative 12, negative 20, and negative 28.

The answer is option D.

Slope measures the rate of change in the dependent variable as the independent variable changes. The greater the slope the steeper the line. Consider the linear function: y = a + bx. b is the slope of the line.

A steeper slope in a graph means that the rate of change is faster.

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The probability that the average weight of a random sample of 10 cars will be 70.7 tons or more is approximately 0.977, or 97.7%.

To calculate the probability that the average weight of a random sample of 10 cars will be 70.7 tons or more, we need to make some assumptions about the population of cars and the sampling process.

Assuming that the weights of cars follow a normal distribution, we can use the central limit theorem to approximate the distribution of sample means. This states that as the sample size increases, the distribution of sample means becomes approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Without knowing the population means and standard deviation, we can use the sample mean and standard deviation as estimates. Let's say we have a sample of 10 cars and their weights have a sample mean of 72 tons and a sample standard deviation of 2 tons. We can calculate the standard error of the mean by dividing the sample standard deviation by the square root of the sample size, which gives us 0.63 tons.

To find the probability that the sample mean is 70.7 tons or more, we need to standardize the distribution of sample means using the z-score formula:

z = (sample mean - population mean) / standard error of the mean

In this case, the population mean is unknown, so we can use the sample mean as an estimate. Plugging in the values, we get:

z = (70.7 - 72) / 0.63 = -2

Using a standard normal distribution table, we can find the probability that a z-score is less than -2, which is approximately 0.023.

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Complete question:

What is the probability that the average weight of a random sample of 10 cars will be 70.7 tons or more if the filling equipment is working properly?

Answer:

3

Step-by-step explanation:

5-2=3

Just do it the other way to find the answer!

I hope this helps!

Answer: x = 3

Step-by-step explanation:

we subtract 2 from both sides, in order to get the variable by itself.

x + 2 (- 2) = 5 (- 2)

x = 3

(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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Assuming that the events of each executive receiving a pay raise are independent, we can use the multiplication rule for independent events to find the probability that all four received a raise.

Let's denote the event that an executive receives a raise by "R". Then, the probability that an executive receives a raise is P(R) = 0.78, and the probability that an executive does not receive a raise is P(not R) = 1 - P(R) = 0.22.

The probability that all four executives receive a raise is:

P(R and R and R and R) = P(R) x P(R) x P(R) x P(R)

= 0.78 x 0.78 x 0.78 x 0.78

= 0.37 or 0.0037 (rounded to 4 decimal places)

Therefore, the probability that all four executives received a raise when they asked for one is approximately 0.0037 or 0.37%.

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Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

The value of t is approximately 2.1315, following a Student's t distribution with 15 degrees of freedom, given P(t < X < 2.1315) = 0.025.

The Student's t distribution is a probability distribution that is used when working with small sample sizes or when the population standard deviation is unknown. It is similar to the normal distribution but has heavier tails, allowing for greater variability.

In this case, we are given that the random variable X follows a Student's t distribution with 15 degrees of freedom. Degrees of freedom in the t distribution represent the number of independent observations used to estimate a parameter. A higher number of degrees of freedom results in a distribution that is closer to the normal distribution.

We are also given that the probability of X lying between t and 2.1315 is 0.025. This probability represents the area under the t distribution curve between those two values. In other words, it is the probability that a randomly selected value from the distribution falls within that range.

To find the value of t, we need to determine the corresponding quantile in the t distribution that corresponds to a probability of 0.025. This quantile can be found using statistical tables or software.

By matching the probability to the quantile, we find that the value of t is approximately 2.1315. This means that there is a 2.5% probability that a randomly selected value from the Student's t distribution with 15 degrees of freedom falls between t and 2.1315.

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When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. Tall wa the buh after the two week is   \(\\26 \frac{2}{5}\).

What is improper fractions?

An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.

12 times 120% + 12

12*120%+12

\($$\begin{aligned}& 120 \% \text { in fractions: } \frac{6}{5} \\& =12 \times \frac{6}{5}+12\end{aligned}$$\)

Follow the PEMDAS order of operations

Multiply and divide (left to right) \($12 \times \frac{6}{5}: \frac{72}{5}$\)

\(=\frac{72}{5}+12$$\)

Add and subtract (left to right) \($\frac{72}{5}+12: \frac{132}{5}$\)

\(=\frac{132}{5}$$\)

Convert improper fractions to mixed numbers: \($\frac{132}{5}=26 \frac{2}{5}$\)

\(=26 \frac{2}{5}$$\)

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Answer:

$29.05

Step-by-step explanation:

First, you have to multiply $19.95 by 2 since he bought 2 shirts that were the same price. 19.95 times 2 is a total of $39.90. It says that he saved $9.10 on both shirts so, in order to see the original price of the shirts, you would have to multiply $9.10 times 2 which is $18.20. Now you need to add 39.90 to 18.20 which is $58.10. You just need to divide that by 2 which will give you $29.05.  Each shirt's orignial price was $29.05

Hope that helps you out :D

One real-world situation that could be modeled by the equation

y = 3x + 5 is when a store charges $3 per pound of apples and an additional $5 for the basket.

In order to solve for the unknown, we need to be given a value for either x or y.

Lets consider an example

If a customer purchases 4 pounds of apples, we can find the total cost by plugging in 4 for x and solving for y:

y = 3x + 5y = 3(4) + 5y = 12 + 5y = 17

Therefore, the total cost of 4 pounds of apples with the $5 basket charge is $17.

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Answer: 60%

Step-by-step explanation:

if you calculate it. It would give you 40% as pastrami and 60% as not pastrami

Answer: 36/90

Step-by-step explanation:

The behavior of the function falls to the left and rises to the right.

Given function  f(x)=x^3-4x^2+7,

Firstly identify the degree of the function which is :

3

Now identify the leading coefficient which is :

1

Now, we know that if the degree is odd then the function ends in opposite direction.

And also the leading coefficient is positive which leads to rise of the graph to the right.

By using the degree and leading coefficient we can determine the behavior of the function by using  below statements ;

1. Even and Positive: Rises to the left and rises to the right.

2. Even and Negative: Falls to the left and falls to the right.

3. Odd and Positive: Falls to the left and rises to the right.

4. Odd and Negative: Rises to the left and falls to the right

So the behavior of the function falls to the left and rises to the right.

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The Percent increase in the number of mobile users in India from last year to this year is 25%.

The percent increase in the number of mobile users in India from last year to this year, we can use the following formula:

Percent Increase = (New Value - Old Value) / Old Value * 100

Given that there were 432 million mobile users last year and it increased to 540 million mobile users this year, we can substitute these values into the formula:

Percent Increase = (540 million - 432 million) / 432 million * 100

Simplifying the calculation:

Percent Increase = 108 million / 432 million * 100

Percent Increase = 0.25 * 100

Percent Increase = 25

Therefore, the percent increase in the number of mobile users in India from last year to this year is 25%.

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Answer:

The side lengths will form a triangle because 6+4 > 7

Step-by-step explanation:

For side lengths, the two smallest sides (ex. 6 and 4) must have a greater sum than then highest side length. Since 6+4 is greater than 7, it creates a triange. If it would have been 5+2 it would not have worked because it needs to be greater than, not less than or equal to.

Answer:

The area of the original garden is x^2 square feet.

The lengths of the sides of the new garden are x + 2 feet and x + 7 feet.

The area of the new garden, in square feet, is

\((x + 2)(x + 7)\)

\( {x}^{2} + 9x + 14\)

1) the area of his garden is, x² feet²

2) the lengths of the sides of the new garden are,

⇒ (x + 2)

⇒ (x + 7)

And, the area of the new garden is,

Area = x² + 9x + 14

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Farmer Bob has a small square garden that is x feet by x feet.

Now,

We know that;

Area of square = Side²

Here, Side = x feet

Hence, the area of his garden is,

Area = x × x

Area = x² feet²

Now, When He decides to add 2 feet to one side of the garden and 7 feet to the other side.

Then, the lengths of the sides of the new garden are,

⇒ (x + 2)

⇒ (x + 7)

Hence, the area of the new garden is,

Area = (x + 2) (x + 7)

Area = x² + 2x + 7x + 14

Area = x² + 9x + 14

Thus, 1) the area of his garden is, x² feet²

2) the lengths of the sides of the new garden are,

⇒ (x + 2)

⇒ (x + 7)

And, the area of the new garden is,

Area = x² + 9x + 14

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